Which table has a constant of proportionality between \( y \) and \( x \) of \( \frac{8}{5} ? \)

To find a table that has a constant of proportionality between \( y \) and \( x \) of \( \frac{8}{5} \), we need to ensure that for every pair of \( (x, y) \) values in the table, the ratio \( \frac{y}{x} \) equals \( \frac{8}{5} \). This means that for any value of \( x \), the corresponding value of \( y \) can be calculated using the formula: \[ y = \frac{8}{5} x \] Let's create a few pairs of \( (x, y) \) values to illustrate this: 1. If \( x = 5 \): \[ y = \frac{8}{5} \times 5 = 8 \] So, the pair is \( (5, 8) \). 2. If \( x = 10 \): \[ y = \frac{8}{5} \times 10 = 16 \] So, the pair is \( (10, 16) \). 3. If \( x = 0 \): \[ y = \frac{8}{5} \times 0 = 0 \] So, the pair is \( (0, 0) \). 4. If \( x = 25 \): \[ y = \frac{8}{5} \times 25 = 40 \] So, the pair is \( (25, 40) \). Now, we can summarize these pairs in a table: \[ \begin{array}{|c|c|} \hline x & y \\ \hline 0 & 0 \\ 5 & 8 \\ 10 & 16 \\ 25 & 40 \\ \hline \end{array} \] In this table, the constant of proportionality \( \frac{y}{x} \) is consistently \( \frac{8}{5} \) for all pairs, confirming that this table represents a proportional relationship with the specified constant.